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Proof step 16 from proof mod-div-ls (previous step)

i1 ≤ (i1 * (j0 + 1)) / j, j0 < j, 0 < j, 0 < i1, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, i0 < i1, 0 ≤ j0, 0 ≤ i2, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j ⊦ (i1 * (j0 + 1)) / j < i1, j0 + 1 = j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: less-mult-div-02 seq: ⊦ 0 < i ∧ 0 < j ∧ i1 < j → (i * i1) / j < i subst: [j, i1, i] → [j, j0 + 1, i1] flags: rewrite, current

Additional information

Used simplifier rules: lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j, j0 + 1, i1